Stellar activity is inherently time variable, therefore simultaneous measurements are necessary to study the correlation between different activity indicators. In this study we compare X-ray fluxes measured within the first all-sky survey conducted by the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) instrument on board the Spectrum-Roentgen-Gamma (SRG) observatory to Ca II H & K, excess flux measurements R+, using observations made with the robotic TIGRE telescope. We created the largest sample of simultaneous X-ray and spectroscopic Ca II H & K observations of late-type stars obtained so far, and in addition, previous measurements of Ca II H & K for all sample stars were obtained. We find the expected correlation between our log(L_X/L_bol) to log(R+) measurements, but when the whole stellar ensemble is considered, the correlation between coronal and chromospheric activity indicators does not improve when the simultaneously measured data are used. A more detailed analysis shows that the correlation of log(L_X/L_bol) to log(R+) measurements of the pseudo-simultaneous data still has a high probability of being better than that of a random set of non-simultaneous measurements with a long time baseline between the observations. Cyclic variations on longer timescales are therefore far more important for the activity flux-flux relations than short-term variations in the form of rotational modulation or flares, regarding the addition of noise to the activity flux-flux correlations. Finally, regarding the question of predictability of necessarily space-based log(L_X/L_bol) measurements by using ground-based chromospheric indices, we present a relation for estimating log(L_X/L_bol) from R+ values and show that the expected error in the calculated minus observed (C-O) log(L_X/L_bol) values is 0.35 dex.
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